Graph - log base 3 of x

$- \log_{3} (x)$

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Find the point at $x = 1$ .

Replace the variable $x$ with $1$ in the expression.

$f (1) = - \log_{3} (1)$

Simplify the result.

Logarithm base $3$ of $1$ is $0$ .

$f (1) = - 0$

Multiply $- 1$ by $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = - \log_{3} (3)$

Simplify the result.

Logarithm base $3$ of $3$ is $1$ .

$f (3) = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$f (3) = - 1$

The final answer is $- 1$ .

$- 1$

Convert $- 1$ to decimal.

$y = - 1$

Find the point at $x = 9$ .

Replace the variable $x$ with $9$ in the expression.

$f (9) = - \log_{3} (9)$

Simplify the result.

Logarithm base $3$ of $9$ is $2$ .

$f (9) = - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$f (9) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (3, - 1), (9, - 2)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 3 & - 1 \\ 9 & - 2 \end{array}$